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Maplets for Calculus receives NSF Grant

Dr. Meade

June 15, 2008: The National Science Foundation (NSF) has awarded a grant to Dr. Douglas Meade of the University of South Carolina and Dr. Philip Yasskin of Texas A&M University to further develop their program "Maplets for Calculus" and to evaluate its effect on calculus teaching. This Course, Curriculum, and Laboratory Improvement (CCLI) grant, awarded by the NSF Division of Undergraduate Education, will last for three years and is one of only 175 new CCLI Phase 1 awards selected as the a result of the evaluation of 875 proposals submitted. Waterloo Maple supported the grant proposal by offering to provide in-kind support in the form of software, travel and technical support.

Dr. Yasskin

Maplets for Calculus is a collection of 94 Maple applets for calculus students and instructors. They provide an interactive graphical user interface for typical examples and exercises on a variety of topics in single-variable calculus. The Maplets for Calculus balance the development of both understanding and technical skills.

The NSF site states,

The Course, Curriculum, and Laboratory Improvement (CCLI) program seeks to improve the quality of science, technology, engineering, and mathematics (STEM) education for all undergraduate students. The program supports efforts to create, adapt, and disseminate new learning materials and teaching strategies, develop faculty expertise, implement educational innovations, assess learning and evaluate innovations, and conduct research on STEM teaching and learning. The program supports three types of projects representing three different phases of development, ranging from small, exploratory investigations to large, comprehensive projects.

The project summary from the grant proposal follows:

Project Summary

This Phase I proposal presents an alternate paradigm to assist students develop a better understanding of fundamental calculus topics and to master the corresponding algebraic skills. This will be realized through the development of a suite of applets with pedagogical benefits exceeding the capabilities of existing on-line homework systems, printed supplements, and textbooks. The existing Maplets for Calculus (M4C) is a collection of over 70 Java applets on topics from single-variable calculus. A maplet is a Java applet that has full access to the Maple computer algebra system. The Maplets for Calculus present algorithmically-generated problems in a graphical user interface and utilize Maple's symbolic computation engine to analytically check student response and to generate appropriate feedback. This is a significant pedagogical improvement over existing online homework systems that make extensive use of multiple choice questions. (A few systems are now connected to Maple or other CAS but do not fully utilize this potential.) M4C goes beyond this by guiding the student step-by-step through the solution process and by checking intermediate steps along the way. Other features found in M4C include the capability of users to input specific problems and real-time generation of 2D and 3D graphics and animations. These features make M4C appropriate for use in a classroom and also in a distance education setting. A major limitation to the current M4C is that it is not convenient for a maplet to record student performance or to access other web-based instructional content from within the applet. These are two specific areas that will be addressed during this project.

General Project Goals and Objectives

  1. Expand the Maplets for Calculus collection to approximately 100 maplets to address all major topics in single-variable calculus and improve their pedagogy, uniformity and functionality.
  2. Design and implement a grading capability for the Maplets for Calculus collection, possibly connecting to an existing homework or course-management system.
  3. Assess the effectiveness of Maplets for Calculus, as individual maplets and as a coordinated learning aid.
  4. Prepare Student and Instructor Guides for Maplets for Calculus in both text and video forms.
  5. Promote Maplets for Calculus, including the assessment results, to the broader mathematics community through publications, presentations, and workshops.

The primary intellectual merit of this Phase I proposal is the creation of pedagogically-motivated custom user interfaces to aid in the teaching of traditional calculus topics. Secondary intellectual merits of the Maplets for Calculus include providing a structured environment for assessing student learning of specific calculus topics (to allow instructors to better focus their instruction) and providing a model for the eventual development of similar collections for basic courses in multivariable calculus, linear algebra, and differential equations.

There are many broader impacts of this project, including i) improved student success -- and satisfaction -- in calculus and ii) improved student preparation for subsequent STEM courses. The benefits will improve student retention in STEM disciplines and, ultimately, improve graduation rates. Students will also benefit from the 24/7 availability of the computer-based teaching tools and the computer's infinite patience to allow students to practice until they master the topic. As already mentioned, summary usage information will allow instructors to better identify problematic topics and to deal with these accordingly. The results of this project will be published (including the posting of a representative sample of maplets in the Digital Classroom Resources section of MathDL) and presented to the general mathematics community at seminars, workshops, and conference presentations.